Chapter 6 aims at accounting for modification by temporal adverbials. The binary approach allows them to operate on different levels of tense structure above S_0. Crucial is the new insight that the relation between modifier A and modified B is not to be expressed as location of A in B but rather as the intersection of A and B. This insight and the flexibility of (deictic) adverbial modification offers the possibility of presenting a structural solution to the Present Perfect puzzle. It also sheds light on the nature of the in/for-test: it explains why terminative sentences with a for-adverbial introduced at a higher level may be regarded as well-formed as opposed to those which require a token interpretation.

This chapter concerns the proportional readings of many and most, for example, where many/most students are smart means ‘the ratio of smart students to non-smart students is high/greater than 1:1’. The authors argue for a GQ analysis of proportional most over Hackl’s adjectival analysis based on distributional differences between relative most (the most P) and proportional most (most P). This GQ analysis is also shown to be supported by morpho-syntactically complex realizations of proportional most, such as the Romanian cei mai mulţi ‘the.MPL more many.MPL’ and cele mai multe ‘the.FPL more many.FPL’. Turning to proportional many, they argue that it shares a syntactic position with cardinal many, namely, SpecMeasP below Det. For the semantics of proportional many, building on Solt’s degree-theoretic approach based on measure functions with a cardinality dimension, the authors propose that measure functions themselves can have a proportional interpretation, based on proportional scales, in which the measure of the entity across a certain dimension is evaluated with respect to the measure of a ‘whole’ in which that entity is included.